- An integer is a factor of another number if it divides the other number with remainder zero.
- A prime number is an integer which has only two factors, 1 and itself.
- A composite number is an integer which has more than two factors.
- A prime factor of a number is a prime number which divides the number with 0 remainder
- A composite number written as a product of prime numbers is called the prime factorization of the number.

**Example:**

**54 = 2 x 3 x 3 x 3.**

## How do you find the prime factorization of a number?

The process of division done at each level can be shown as branches in a factor tree, one branch showing the prime divisor and the other branch leading to the quotient obtained on division.

## Example for finding the prime factorization of a number.

Since 96 is even number, it is divisible by 2. Hence the first division of 96 by 2 gives the factors as

**96 = 2 x 48.**

The first branch of the factor tree will look like,

96

/\

/ \

Prime factor →

**2**48

The quotient 48 is again divisible by 2 and 48 = 2 x 24. The results of successive divisions by prime factors can be written as

**24 = 2 x 12**

12 = 2 x 6

6 = 2 x 3

12 = 2 x 6

6 = 2 x 3

Quotient 3 is a prime number and hence the division cannot be continued. The entire process can be shown as a prime factorization tree as follows:

96

/\

/ \

Prime factor →

**2**48

/\

/ \

Prime factor →

**2**24

/\

/ \

Prime factor →

**2**12

/\

/ \

Prime factor →

**2**6

/\

/ \

Prime factor →

**2 3**← Prime factor.

The Prime factorization of

**96 = 2 x 2 x 2 x 2 x 2 x 3**or using exponents

**96 = 2**

^{5}x 3.